i'm with caz, border terriers are great little dogs, i have a border cross and he is a little star, absolutely fantastic with my DD (2). He is only 8 months old. He is not big but not small and dainty so is pretty robust.
Don't be fooled by a small dog not needing long walks, mine would walk all day if he were given the chance, but im really crap and it is feast or famine in this house im afraid. So whilst he loves his walks, he is happy with a play in the garden and some rough and tumble with me. At least he has never said other wise
Schnauzers are nice, on the whole i think they have good temprements. Daschunds are nice too, but they do have a tendancy to bark, bark and then bark some more. Not all of them, but i think it is a breed trait, a friend of mine has just got a miniture dachsy pup, funny looking thing it is, but a fantastic little character.
I honestly couldnt recommend the border terrier more, and they are not quite so expensive as the other breeds. We paid £200 for our cross breed (far to much) but we chose him because he had been bred in the home. That is another really important thing, if at all possible, go for a dog that has been bred in a home environment, it makes training so much easier.
As far as training goes, there are plenty of classes on offer, which are great fun and your children are old enough to enjoy that too. I would advise getting a cage, as this is excellent for toilet training and provides a place of sanctuary for the dog (and you when youve had enough of him)> Those are relatively cheap. Schnausers will need to be professionally groomed to, so remember to factor that into your equation. Do take time to make sure you make the right choice for you breed wise, but it does sound like you are being sensible about it. BOB - my little "borderpatterdale" is like my shadow and follows me everywhere. He does kick off when i leave him but he is a dog, he has to live with it and get used to it. Being small though, i tend to take him most places with me. He is our first small dog, we used to have rotties but i certainly wouldnt recommend those to a first time dog owner with young children
oh by the way - im half tempted to get a second dog, so reading your thread has made me "broody"